I've been testing out Live Mesh for a few weeks now. I'll avoid any discussion of specific features as I'm guessing it's mostly NDA'd. It is hard to describe what it is in a single sentence. But to be honest I think that's OK since it is a developer beta.
I started out using Mesh for some basic file storage (on a few meg). With that experience being successful I've now moved on to syncing hundred of megabytes of files with the Mesh.
I'm also starting to see some interesting possibilities with the Mesh framework - beyond the super basic files/RDP scenarios showcased in the original demo. Once I get some other projects out of the way I might try my hand at a Mesh enabled application.